On the phase-field algorithm for distinguishing connected regions in digital model

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2024-08-13 DOI:10.1016/j.enganabound.2024.105918

引用次数: 0

Abstract

In this paper, we propose a novel model for the discrimination of complex three-dimensional connected regions. The modified model is grounded on the Allen–Cahn equation. The modified equation not only maintains the original interface dynamics, but also avoids the unbounded diffusion behavior of the original Allen–Cahn equation. This advantage enables us to accurately populate and extract the complex connectivity region of the target part. The model is discretized employing a semi-implicit Crank–Nicolson scheme, ensuring second-order accuracy in both time and space. This paper provides a rigorous proof of the unconditional energy stability of our method, thereby affirming the numerical stability and the physical rationality of the solution. We validate the discriminative ability of the proposed model for 3D complex connected regions.

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论区分数字模型中连接区域的相场算法

在本文中，我们提出了一个用于辨别复杂三维连接区域的新模型。修正模型以 Allen-Cahn 方程为基础。修正后的方程不仅保持了原始的界面动力学，而且避免了原始 Allen-Cahn 方程的无约束扩散行为。这一优势使我们能够精确地填充和提取目标零件的复杂连接区域。该模型采用半隐式 Crank-Nicolson 方案离散化，确保了时间和空间的二阶精度。本文严格证明了我们方法的无条件能量稳定性，从而肯定了求解的数值稳定性和物理合理性。我们验证了所提模型对三维复杂连接区域的判别能力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.